Yazar "Benaissa, Bouharket" seçeneğine göre listele

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    Bullen-Mercer type inequalities for the h-convex function with twice differentiable functions
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Huseyin
    Bullen-type inequalities for h-convex functions using conformable fractional operators are established in this study on the cone of twice-differentiable functions. This is a novel fractional version of the existing Bullen-type inequalities with simple procedures using the B-function. Furthermore, new results on Bullen-type inequalities are presented for several specific cases of convexity, generalizing existing inequalities known in the literature.
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    Discussion on $(k, s)$-Riemann Liouville fractional integral and applications
    (Hacettepe Üniversitesi, 2024) Benaissa, Bouharket; Sarıkaya, Mehmet Zeki
    In this paper we present the correct version of Theorem 2.2 in [$(k; s)$-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat. \textbf{45} (1), 77 - 89, 2016] and prove it.
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    GENERAL ((k, p ) , ψ)-HILFER FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2024) Benaissa, Bouharket; Budak, Huseyin
    The main motivation of this study is to establish a general version of the RiemannLiouville fractional integrals with two exponential parameters k and p called ((k, p),psi)-Hilfer fractional integrals which is determined over the k-gamma function. We first prove that these operators are well-defined, continuous and have semi-group property. Then, particularly, we present the harmonic, geometric and arithmetic (k, p), psi-Hilfer fractional integrals. Moreover, some special cases relating to general ((k, p),psi)-Riemann-Liouville fraction integrals are given.
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    General (k, p)-Riemann-Liouville fractional integrals
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Budak, Hüseyin
    The main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p which is determined over the (k, p)-gamma function. In particular, we present the harmonic, geometric and arithmetic (k, p)- Riemann-Liouville fractional integrals. When p = k, these integrals reduce to k-Riemann-Liouville fractional integrals. Some formulas relating to general (k, p)-Riemann-Liouville fraction integrals are also given.
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    A GENERALIZATION OF WEIGHTED BILINEAR HARDY INEQUALITY
    (Publishing House of the Romanian Academy, 2021) Benaissa, Bouharket; Zeki Sarıkaya, Mehmet
    In this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using weighted mean operators S:= (Sf)w g, where f nonnegative integrable function with two variables on ? = (0,+?)×(0,+?), defined by with where w is a weight function and g is a nonnegative continuous function on (0,+?). © 2021, Publishing House of the Romanian Academy. All rights reserved.
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    Hermite-Hadamard type inequalities for new conditions on h-convex functions via ? -Hilfer integral operators
    (Springer Basel Ag, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Hüseyin
    We employ a new function class called B-function to create a new version of fractional Hermite-Hadamard and trapezoid type inequalities on the right-hand side that involves h-convex and psi -Hilfer operators. We also provide new midpoint-type inequalities using h-convex functions.
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    Hermite-Hadamard-Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators
    (Springer, 2025) Azzouz, Noureddine; Benaissa, Bouharket; Budak, Hueseyin; Demir, Izzettin
    In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of psi-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on psi. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and H & ouml;lder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann-Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.
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    MILNE-TYPE INEQUALITIES FOR h- CONVEX FUNCTIONS
    (Michigan State Univ Press, 2024) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    Milne-type inequalities for h- convex functions involving conformable operators are established. Additionally, new results are presented that generalize various known inequalities.
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    Milne-type inequalities for third differentiable and h-convex functions
    (Springer, 2025) Benaissa, Bouharket; Budak, Huseyin
    This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.
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    MORE ON REVERSE OF HOLDER'S INTEGRAL INEQUALITY
    (Kangwon-Kyungki Mathematical Soc, 2020) Benaissa, Bouharket; Budak, Hüseyin
    In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Holder inequality. We note that many existing inequalities related to the Holder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].
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    On generalized ψ-conformable calculus: Properties and inequalities
    (Univ Nis, Fac Sci Math, 2024) Azzouz, Noureddine; Benaissa, Bouharket; Budak, Huseyin
    In this paper, we first introduce a new fractional derivatives and integrals called generalized psi-conformable derivative and generalized psi-conformable integral operators, respectively. We also show that these operators generalize various well-known fractional integral operators. Then, we present several properties of these operators including semi-group property. Moreover, we apply these operators to obtain a new Hermite-Hadamard-type inequality for convex functions. Furthermore, we obtain corresponding midpoint and trapezoid type inequalities for functions whose derivatives in absolute value are convex.
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    On Milne Type Inequalities For h-Convex Functions Via Conformable Fractional Integral Operators
    (Tsing Hua Univ, Dept Mathematics, 2025) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    In this study, Milne-type inequalities for h-convex functions involving conformable operators are established. In addition, new results are presented that generalize various inequalities known in the literature.
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    On some Grüss-type inequalities via k-weighted fractional operators
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarıkaya, Mehmet Zeki
    In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr & uuml;ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.
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    On some new Hardy-type inequalities
    (Wiley, 2020) Benaissa, Bouharket; Sarıkaya, Mehmet Zeki; Senouci, Abdelkader
    In this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operators S-1 := (S-1)(g)(w) and S-2 := (S-2)(g)(w) defined by S-1(x) = 1/W(x) integral(x)(a) w(t)g(f(t))dt, S-2(x) = integral(x)(a) w(t)/W(t)g(f(t))dt, with W(x) = integral(x)(0) w(t)dt, for x is an element of(0,+infinity), where w is a weight function and g is a real continuous function on (0,+infinity).
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    On the refinements of some important inequalities with a finite set of positive numbers
    (Wiley, 2024) Benaissa, Bouharket; Sarıkaya, Mehmet Zeki
    In this research, a novel method for enhancing the Holder-Iscan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Holder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function phi$$ \phi $$, an entirely new category of classical inequalities emerges for both Holder and mean power inequalities.
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    Simpson's quadrature formula for third differentiable and s-convex functions
    (Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarikaya, Mehmet Zeki
    This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for various convexity cases.
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    Some Hardy-type integral inequalities involving functions of two independent variables
    (Springer, 2021) Benaissa, Bouharket; Sarıkaya, Mehmet Zeki
    In this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operatorsS(1) := S1(w) f and S-2 := S-2(w) f defined by S-1(x, y) = 1/W(x)W(y) integral(x)(x/2) integral(y)(y/2) w(t)w(s) f (t, s)dsdt, and S-2(x, y) = integral(x)(x/2) integral(y)(y/2) w(t)w(s)/W(t)W(s) f (t, s)dsdt, with W (z) = integral(z)(0) w(r)dr f or z is an element of (0,+infinity), where w is a weight function.
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    Weighted fractional inequalities for new conditions on h-convex functions
    (Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Hüseyin
    We use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.